221_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

221_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.8-2.12.qxd 9/25/08 11:43 AM Page 215 SECTION 2.8 Impact Loading Problem 2.8-5 Solve the preceding problem if the block weighs W 1.0 lb, h 12 in., and k Solution 2.8-5 0.5 lb/in. Block dropping onto a spring (a) MAXIMUM SHORTENING OF THE SPRING W k dst 1.0 lb 0.5 lb/in. Eq. (2-53): dmax 2.0 in. dst c 1 + a 1 + 9.21 in. 2h 1/2 bd dst ; (b) IMPACT FACTOR (EQ. 2-61) dmax 9.21 in. dst 2.0 in. 4.6 ; Impact factor W 1.0 lb h 12 in. k 0.5 lb/in. Problem 2.8-6 A small rubber ball (weight W 450 mN) is attached by a rubber cord to a wood paddle (see figure). The natural length of the cord is L0 200 mm, its crosssectional area is A 1.6 mm2, and its modulus of elasticity is E 2.0 MPa. After being struck by the paddle, the ball stretches the cord to a total length L1 900 mm. What was the velocity v of the ball when it left the paddle? (Assume linearly elastic behavior of the rubber cord, and disregard the potential energy due to any change in elevation of the ball.) Solution 2.8-6 Rubber ball attached to a paddle WHEN THE RUBBER CORD IS FULLY STRETCHED: U EAd2 2L0 EA (L 2L0 1 L0)2 CONSERVATION OF ENERGY KE 2 v2 g 9.81 m/s E 2.0 MPa A 1.6 mm2 L0 200 mm L1 900 mm W 450 mN WHEN THE BALL LEAVES THE PADDLE KE Wv2 2g v U Wv2 2g gEA (L WL0 1 (L1 EA (L1 2L0 gEA A WL0 L0) L0)2 L0)2 ; (9.81 m/s2) (2.0 MPa) (1.6 mm2) A (450 mN) (200 mm) 13.1 m/s ; SUBSTITUTE NUMERICAL VALUES: v (700 mm) 215 ...
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